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  • Articles  (67)
  • Oxford University Press  (67)
  • American Chemical Society
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  • 2010-2014  (67)
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  • 2011  (67)
  • Logic Journal of the IGPL  (16)
  • 283
  • Mathematics  (67)
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  • Articles  (67)
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  • Oxford University Press  (67)
  • American Chemical Society
  • BioMed Central
  • Nature Publishing Group
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  • 2010-2014  (67)
  • 1990-1994
  • 1955-1959
  • 1945-1949
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  • Mathematics  (67)
  • Geosciences
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • 1
    Publication Date: 2011-11-24
    Description: We present a framework for the representation and resolution of first-order unification problems and their abstract syntax in a variable-free relational formalism which is an executable variant of the Tarski-Givant relation algebra and of Freyd’s allegories restricted to the fragment necessary to compile and run logic programs. We develop a decision procedure for validity of relational terms, which corresponds to solving the original unification problem. The decision procedure is carried out by a conditional relational-term rewriting system. There are advantages over classical unification approaches. First, cumbersome and underspecified meta-logical procedures (name clashes, substitution, etc.) and their properties (invariance under substitution of ground terms, equality’s congruence with respect to term forming, etc.) are captured algebraically within the framework. Second, other unification problems can be accommodated, for example, existential quantification in the logic can be interpreted as a new operation whose effect is to formalize the costly and error prone handling of fresh names (renaming apart).
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
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  • 2
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    Oxford University Press
    Publication Date: 2011-11-24
    Description: The original motivation of D. Gabbay’s concept of Fibring concerned the combination of logics, and initially it involved the syntactic introduction of modals into formulations of intuitionistic logic in which modals are syntactically absent. We show, using the notion of structural modals that there are many modals of intuitionism, and logics for subjunctive and epistemic conditionals which are not syntactically evident in our best formulations of them. We discuss some cases when the attempt to make them syntactically evident can have undesirable consequences.
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  • 3
    Publication Date: 2011-11-24
    Description: Basic narrowing is a restricted form of narrowing which constrains narrowing steps to a set of unblocked (or basic) positions. In this work, we study the modularity of termination of basic narrowing in hierarchical combinations of TRSs, which provides new algorithmic criteria to prove termination of basic narrowing. Basic narrowing has a number of important applications including equational unification in canonical theories. Another application is analyzing termination of narrowing by checking the termination of basic narrowing, as done in pioneering work by Hullot. As a particularly interesting application, we consider solving equations modulo a theory that is given by a TRS, and then distill a number of modularity results for the decidability of equational unification via the modularity of basic narrowing (completeness and) termination.
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  • 4
    Publication Date: 2011-11-24
    Description: Bounded Second-Order Unification is a decidable variant of undecidable Second-Order Unification. Stratified Context Unification is a decidable restriction of Context Unification, whose decidability is a long-standing open problem. This paper is a join of two separate previous, preliminary papers on NP-completeness of Bounded Second-Order Unification and Stratified Context Unification. It clarifies some omissions in these papers, joins the algorithmic parts that construct a minimal solution, and gives a clear account of a method of using singleton tree grammars for compression that may have potential usage for other algorithmic questions in related areas.
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  • 5
    Publication Date: 2011-11-24
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  • 6
    Publication Date: 2011-11-24
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  • 7
    Publication Date: 2011-11-24
    Description: Recently, ontologies emerge in various domains and different communities. For instance, in the database area, they are used to facilitate data exchange and integration, in the Semantic Web field, to describe terms, retrieve information and interconnect Web services. Several ontology languages and formalisms are given (OWL, PLIB, etc.). Due to the ontology evolution, various applications manipulate a huge amount of ontological data (data referencing ontologies). Consequently, they cannot fit in the main memory. To offer efficient storage and querying mechanisms of these data, academicians and industrials proposed database solutions storing in the same repository data and the ontology describing their senses. Such database is called ontology-based databases (OBDB). Despite this trend, no design methodology adapted to OBDB exists contrary to traditional databases, where two main methodologies inspired from: Codd-Armstrong and Chen research efforts are proposed. Developing a design methodology for OBDB constitutes a crucial challenge for the success of OBDB applications. Similarities between conceptual models and ontologies recently identified motivate us to propose an OBDB design methodology inspired from the existing ones. To do so, we first describe in details these similarities and differences. Secondly, we propose an ontology-driven methodology to derive a normalized logical schema of a database from domain ontology whose each class contains a set of FDs. Finally, a prototype implementing our methodology is presented.
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  • 8
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    Oxford University Press
    Publication Date: 2011-11-24
    Description: Unification was originally introduced in automated deduction and term rewriting, but has recently also found applications in other fields. In this article, we give a survey of the results on unification obtained in two closely related, yet different, application areas of unification: description logics and modal logics.
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  • 9
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    Oxford University Press
    Publication Date: 2011-11-24
    Description: The modern view of logical reasoning as modeled by a consequence operator (instead of simply by a set of theorems) has allowed for huge developments in the study of logic as an abstract discipline. Still, it is unable to explain why it is often the case that the same designation is used, in an ambiguous way, to describe several distinct modes of reasoning over the same logical language. A paradigmatic example of such a situation is ‘modal logic’, a terminology which can encompass reasoning over Kripke frames, but also over Kripke models, and in any case either locally (at a fixed world) or globally (at all worlds). Herein, we adopt a novel abstract notion of logic presented as a lattice-structured hierarchy of consequence operators, and explore some common proof-theoretic and model-theoretic ways of presenting such hierarchies through a collection of meaningful examples. In order to illustrate the usefulness of the notion of hierarchical consequence operators we address a few questions in the theory of combined logics, where a suitable abstract presentation of the logics being combined is absolutely essential. We show how to define the operation, in general, and we achieve a number of interesting preservation results for fibring within the context of 2 -hierarchies.
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  • 10
    Publication Date: 2011-11-24
    Description: This paper focuses on three research questions which are connected with combinations of modal logics: (i) Under which conditions can (frame-) completeness (and related properties) be transferred from a propositional modal logic (PML) to its quantificational counterpart (QML)? (ii) Does (frame-) completeness generally transfer from monomodal QMLs to their multimodal combination? (iii) Can completeness be transferred from QMLs with rigid designators to those with non-rigid designators? The paper reports some recent results on these questions and provides some new results.
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